# angular acceleration of an arm

by tristanmagnum
Tags: acceleration, angular
 P: 44 F=ma says that an object with mass m will experience acceleration a under force F. The acceleration you obtained belong to which object? Arm? Ball? Which mass should you use then?
 P: 44 the mass of the arm? correct
 P: 26 add the two masses up.
 P: 44 Ops! Part B appeared to be more tricky than I initially thought. You can forget using F=ma to solve it. May I know where you get this problem? There are a few assumptions to be made in order to solve this problem. Still, it takes plenty of steps to get the final answer. First, you must draw the free body diagram with the arm and the ball as the system. This will help you to picture how each components contribute to the τ (net torque) of the system. With τ=Iα，where I is the moment of inertia, α is the angular acceleration, you will be able to get the value of τ, provided you know how to calculate I. (refer to your textbook on moment of inertia for uniform rod) τ(tricep) - τ(arm) - τ(ball) = τ(net) Using the above equation, you will be able to solve for τ(tricep) and in turn, F(tricep). You will need this in your workout: τ=Fr where r is the distance from the pivot point to the point where force is applied.
 P: 26 How can you get the moment of inertia if you dont have the radius of the ball? 2/5mr^2
 P: 26 i guess, I = ∫ r2d(m) could work
 P: 44 Maybe there is no need to calculate moment of inertia. Use τ=Fr to calculate τ(net) will do. F can be obtained through F=ma and r can be obtained through finding the centre of mass of the system. Anyways, it is up to the original question raiser to do the math.
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P: 9,212
 Quote by Periapsis How can you get the moment of inertia if you dont have the radius of the ball? 2/5mr^2
You can treat the ball as a point mass, making its MI about the arm's axis easy. The Mi of the arm is obtained by treating it as a rod rotated about one end.
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